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Kotlin-based LeetCode algorithm problem solutions, regularly updated
1510\. Stone Game IV
Hard
Alice and Bob take turns playing a game, with Alice starting first.
Initially, there are `n` stones in a pile. On each player's turn, that player makes a _move_ consisting of removing **any** non-zero **square number** of stones in the pile.
Also, if a player cannot make a move, he/she loses the game.
Given a positive integer `n`, return `true` if and only if Alice wins the game otherwise return `false`, assuming both players play optimally.
**Example 1:**
**Input:** n = 1
**Output:** true
**Explanation:** Alice can remove 1 stone winning the game because Bob doesn't have any moves.
**Example 2:**
**Input:** n = 2
**Output:** false
**Explanation:** Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).
**Example 3:**
**Input:** n = 4
**Output:** true
**Explanation:** n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).
**Constraints:**
* 1 <= n <= 105